I have performed several analysis to find which pathways are enriched in my data set, but they don't test activation or inactivation.

After observing the expression of one of those pathways I can observe an increase of the expression, however I was wondering if this implies activation of the pathway. I calculated the enrichment score (using GSEA) of the pathway but it is not designed to test if the pathway is activated or not, is it?

Is there any tool, to test activation/inactivation of a pathway?

I have found SIPA, ASSIGN, DART (on Bioconductor), but they all relay on KEGG, and I would like to be able to use also other pathways from Reactome or Biocarta. I would prefer using R but any tool/method is welcome.

Gene expression data can't tell that a pathway or even a gene product is active at the time of the measurement. Since many biological processes are regulated at the post-transcriptional level, expression data should be used for candidate selection to do further experimental tests. You could refine the hypothesis using bioinformatics tools but ultimately, you'll have to experimentally validate that the pathway of interest is (in)activated under the conditions you're testing.

Before validating experimentally I would like to reduce the list of pathways.
I thought that if Ingenuity Pathway Analysis offers an activation score, with only transcriptomic data, there could be other methods available. Even if such a tool predicts a pathway as activated/inactivated and it isn't it would be even more interesting for the descriptive study I am doing.

Maybe you can use a simple way to predict whether the pathway(gene set) is activated or inactivated.
If you have a gene set S, and It contains M genes. And from your data set , you will get N differently expressed genes. Then you can use Binomial test to evaluate whether this pathway(gene set)' gene is significantly DE.
By the way, you can use Z value from the test to be inactivated score.
Wish helpful for you.

The question is not if a gene set is significantly differently expressed, there is already software for that (like GSVA from Bioconductor), but if it is activated. Ingenuity Pathway Analysis uses a Z value to test for activation/inactivation, however I am concerned it doesn't take into account inhibitors and enhancers as such. This test you propose wouldn't take it into account neither if I understood it correctly.